Zooming In On Figures

Unit Overview

Type of Unit: Concept; Project

Length of Unit: 18 days and 5 days for project

Prior Knowledge

Students should be able to:

  • Find the area of triangles and special quadrilaterals.
  • Use nets composed of triangles and rectangles in order to find the surface area of solids.
  • Find the volume of right rectangular prisms.
  • Solve proportions.

Lesson Flow

  • After an initial exploratory lesson that gets students thinking in general about geometry and its application in real-world contexts, the unit is divided into two concept development sections: the first focuses on two-dimensional (2-D) figures and measures, and the second looks at three-dimensional (3-D) figures and measures.
  • The first set of conceptual lessons looks at 2-D figures and area and length calculations. Students explore finding the area of polygons by deconstructing them into known figures. This exploration will lead to looking at regular polygons and deriving a general formula. The general formula for polygons leads to the formula for the area of a circle. Students will also investigate the ratio of circumference to diameter ( pi ). All of this will be applied toward looking at scale and the way that length and area are affected. All the lessons noted above will feature examples of real-world contexts.
  • The second set of conceptual development lessons focuses on 3-D figures and surface area and volume calculations. Students will revisit nets to arrive at a general formula for finding the surface area of any right prism. Students will extend their knowledge of area of polygons to surface area calculations as well as a general formula for the volume of any right prism. Students will explore the 3-D surface that results from a plane slicing through a rectangular prism or pyramid. Students will also explore 3-D figures composed of cubes, finding the surface area and volume by looking at 3-D views.
  • The unit ends with a unit examination and project presentations.
Subject:
Mathematics, Geometry
Level:
Middle School
Grade:
7
Tags:
Building, Right Prisms, Circumference, Scale, Surface Area, Formulas, Geometry, Pyramids, Presentations, Planar Slices, 7th Grade Mathematics, Cubes, Architecture, Concepts, Ratio, Pi, Cones, Circles, Diameter, Buildings, Volume, Scale Drawing, Models, Area, Problems, Prisms, Cylinders, Design, 2D, Rectangles, Polygons, Triangles, 3d
License:
http://creativecommons.org/licenses/by-nc/4.0/

Lesson 2

· Scissors (one pair for each student)

· Rulers (one for each student)

· Print copies of Area of Regular Polygons (one for each student). Print out, cut apart, and laminate if desired.

Lesson 3

  • Graphing chart paper that is 12-inch by 12-inch with 1-inch spacing (one for each student)
  • A 12-inch by 12-inch piece of cardboard (one for each student)
  • Glue (one for each pair of students)
  • Ruler (one for each student)

Lesson 4

· String (several spools for the class)

· Rulers (one for each student)

· Scissors (one for each student)

Lesson 6

Ruler (one for each student)

Lesson 7

· Centimeter grid paper (one for each student)

· Ruler (one for each student)

· Compass (one for each student)

Lesson 8

· Base sheets for project (one for each student)

· Square foot cardboard pieces to mount base sheets on (one for each student)

· Rulers (one for each pair of students)

· Protractors (one for each pair of students)

Lesson 16

Students’ centimeter grid layout to draw the nets

Lesson 17

· Origami cubes

· Cardboard

Lesson 18

· Centimeter grid layout

· 1-inch grid paper

· Rulers

· Scissors, tape, protractors (available as needed)

Unit 4 Zooming In On Figures